There are only two periods of night present. The explanation is that three days and three nights is simply an idiom for three days. I think Esther might give another explicit example of this, but I don't have time to check right this minute. All we need to know is that Christ said to his disciples, "Thus it is written, that the Christ should suffer and on the third day rise from the dead" (Luke 24:46). Based on this and other expressions related to the duration between his death and resurrection, any understanding of "three days and three nights" is what must be reconciled to that and not the other away around.
Some people who insist that Jesus died on some day other than Friday, account for the addition of extra days by saying the day he was buried was the zeroeth day. This is not how they reckoned time. Leviticus 23:15-16 is a good counterexample.
"You shall count seven full weeks from the day after the Sabbath, from the day that you brought the sheaf of the wave offering. You shall count fifty days to the day after the seventh Sabbath. Then you shall present a grain offering of new grain to the Lord."
So it can be seen that though Sunday to Sunday is for us is fourty-nine days later, the Hebrews numbered it fifty days, because they reckoned the starting day as the first day and not a day zero.